A $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ Effective Hamiltonian Generator
Yi Jiang1,2, Zhong Fang1, and Chen Fang1,3,4*
1Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 2University of Chinese Academy of Sciences, Beijing 100049, China 3Songshan Lake Materials Laboratory, Dongguan 523808, China 4Kavli Institute for Theoretical Sciences, Chinese Academy of Sciences, Beijing 100190, China
Abstract：A $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ effective Hamiltonian is important for theoretical analysis in condensed matter physics. Based on the kdotp-symmetry package, we develop an upgraded package named as kdotp-generator. This generator takes in arbitrary magnetic symmetries with their representations and returns symmetry-allowed $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ Hamiltonians. Using this package, we calculate $\boldsymbol{k}$$\cdot$$\boldsymbol{p}$ Hamiltonians for irreducible co-representations in 1651 magnetic space groups up to the third order, and their linear coupling to external fields including the electromagnetic field and the strain tensor. We hope that the package will facilitate related research in the future.
Aroyo M I, Perez-Mato J, Orobengoa D, Tasci E, de la Flor G, and Kirov A 2011 Bulg. Chem. Commun.43 183
[37]
Elcoro L, Wieder B J, Song Z, Xu Y, and Bradlyn B 2020 arXiv:2010.00598 [cond-mat.mes-hall]
[38]
Bradley C and Cracknell A 2009 The Mathematical Theory of Symmetry in Solids: Representation Theory for Point Groups and Space Groups (Oxford: Oxford University Press)
[39]
Recently, the Bilbao website has updated the coirreps of 1651 MSGs.[37] While we use our homemade code to generate the coirreps of MSGs, the matrix forms are not exactly the same as those on the Bilbao website, especially for some type-3 MSGs. This is because the explict forms of high-dimensional representation depend on the choice of gauge.
[40]
Yu Z M, Zhang Z, Liu G B, Wu W, and Li X P 2021 arXiv:2102.01517 [cond-mat.mes-hall]
2021, Vol. 38 
